The contribution of this paper includes two aspects. First, we study the lower bound complexity for the minimax optimization problem whose objective function is the average of $n$ individual smooth component functions. We consider Proximal Incremental First-order (PIFO) algorithms which have access to gradient and proximal oracle for each individual component. We develop a novel approach for constructing adversarial problems, which partitions the tridiagonal matrix of classical examples into $n$ groups. This construction is friendly to the analysis of incremental gradient and proximal oracle. With this approach, we demonstrate the lower bounds of first-order algorithms for finding an $\varepsilon$-suboptimal point and an $\varepsilon$-stationary point in different settings. Second, we also derive the lower bounds of minimization optimization with PIFO algorithms from our approach, which can cover the results in \citep{woodworth2016tight} and improve the results in \citep{zhou2019lower}.

Machine learning (ML) is successful in achieving human-level performance in various fields. However, it lacks the ability to explain an outcome due to its black-box nature. While existing explainable ML is promising, almost all of these methods focus on formatting interpretability as an optimization problem. Such a mapping leads to numerous iterations of time-consuming complex computations, which limits their applicability in real-time applications. In this paper, we propose a novel framework for accelerating explainable ML using Tensor Processing Units (TPUs). The proposed framework exploits the synergy between matrix convolution and Fourier transform, and takes full advantage of TPU's natural ability in accelerating matrix computations. Specifically, this paper makes three important contributions. (1) To the best of our knowledge, our proposed work is the first attempt in enabling hardware acceleration of explainable ML using TPUs. (2) Our proposed approach is applicable across a wide variety of ML algorithms, and effective utilization of TPU-based acceleration can lead to real-time outcome interpretation. (3) Extensive experimental results demonstrate that our proposed approach can provide an order-of-magnitude speedup in both classification time (25x on average) and interpretation time (13x on average) compared to state-of-the-art techniques.

Policy optimization methods remain a powerful workhorse in empirical Reinforcement Learning (RL), with a focus on neural policies that can easily reason over complex and continuous state and/or action spaces. Theoretical understanding of strategic exploration in policy-based methods with non-linear function approximation, however, is largely missing. In this paper, we address this question by designing ENIAC, an actor-critic method that allows non-linear function approximation in the critic. We show that under certain assumptions, e.g., a bounded eluder dimension $d$ for the critic class, the learner finds a near-optimal policy in $O(\poly(d))$ exploration rounds. The method is robust to model misspecification and strictly extends existing works on linear function approximation. We also develop some computational optimizations of our approach with slightly worse statistical guarantees and an empirical adaptation building on existing deep RL tools. We empirically evaluate this adaptation and show that it outperforms prior heuristics inspired by linear methods, establishing the value via correctly reasoning about the agent's uncertainty under non-linear function approximation.

This paper presents and discusses algorithms, hardware, and software architecture developed by the TEAM CoSTAR (Collaborative SubTerranean Autonomous Robots), competing in the DARPA Subterranean Challenge. Specifically, it presents the techniques utilized within the Tunnel (2019) and Urban (2020) competitions, where CoSTAR achieved 2nd and 1st place, respectively. We also discuss CoSTAR's demonstrations in Martian-analog surface and subsurface (lava tubes) exploration. The paper introduces our autonomy solution, referred to as NeBula (Networked Belief-aware Perceptual Autonomy). NeBula is an uncertainty-aware framework that aims at enabling resilient and modular autonomy solutions by performing reasoning and decision making in the belief space (space of probability distributions over the robot and world states). We discuss various components of the NeBula framework, including: (i) geometric and semantic environment mapping; (ii) a multi-modal positioning system; (iii) traversability analysis and local planning; (iv) global motion planning and exploration behavior; (i) risk-aware mission planning; (vi) networking and decentralized reasoning; and (vii) learning-enabled adaptation. We discuss the performance of NeBula on several robot types (e.g. wheeled, legged, flying), in various environments. We discuss the specific results and lessons learned from fielding this solution in the challenging courses of the DARPA Subterranean Challenge competition.

With mathematical optimization, companies can capture the key features of their business problems in an optimization model and can generate optimal solutions (which are used as the basis to make optimal decisions). Data scientists with some basic mathematical programming skills can easily learn how to build, implement, and maintain mathematical optimization applications. The Gurobi Python API borrows ideas from modeling languages, enabling users to deploy and solve mathematical optimization models with scripts that are easy to write, read, and maintain. Such modules can even be embedded in decision support systems for production-ready applications.

Lawrence Livermore National Laboratory (LLNL) computer scientists have developed a new framework and an accompanying visualization tool that leverages deep reinforcement learning for symbolic regression problems, outperforming baseline methods on benchmark problems. The paper was recently accepted as an oral presentation at the International Conference on Learning Representations (ICLR 2021), one of the top machine learning conferences in the world. The conference takes place virtually May 3-7. In the paper, the LLNL team describes applying deep reinforcement learning to discrete optimization--problems that deal with discrete "building blocks" that must be combined in a particular order or configuration to optimize a desired property. The team focused on a type of discrete optimization called symbolic regression--finding short mathematical expressions that fit data gathered from an experiment.

IMAGE: A barren plateau is a trainability problem that occurs in machine learning optimization algorithms when the problem-solving space turns flat as the algorithm is run. LOS ALAMOS, N.M., March 19, 2021--Many machine learning algorithms on quantum computers suffer from the dreaded "barren plateau" of unsolvability, where they run into dead ends on optimization problems. This challenge had been relatively unstudied--until now. Rigorous theoretical work has established theorems that guarantee whether a given machine learning algorithm will work as it scales up on larger computers. "The work solves a key problem of useability for quantum machine learning. We rigorously proved the conditions under which certain architectures of variational quantum algorithms will or will not have barren plateaus as they are scaled up," said Marco Cerezo, lead author on the paper published in Nature Communications today by a Los Alamos National Laboratory team.

Interpretability in machine learning (ML) is crucial for high stakes decisions and troubleshooting. In this work, we provide fundamental principles for interpretable ML, and dispel common misunderstandings that dilute the importance of this crucial topic. We also identify 10 technical challenge areas in interpretable machine learning and provide history and background on each problem. Some of these problems are classically important, and some are recent problems that have arisen in the last few years. These problems are: (1) Optimizing sparse logical models such as decision trees; (2) Optimization of scoring systems; (3) Placing constraints into generalized additive models to encourage sparsity and better interpretability; (4) Modern case-based reasoning, including neural networks and matching for causal inference; (5) Complete supervised disentanglement of neural networks; (6) Complete or even partial unsupervised disentanglement of neural networks; (7) Dimensionality reduction for data visualization; (8) Machine learning models that can incorporate physics and other generative or causal constraints; (9) Characterization of the "Rashomon set" of good models; and (10) Interpretable reinforcement learning. This survey is suitable as a starting point for statisticians and computer scientists interested in working in interpretable machine learning.

We consider the vector embedding problem. We are given a finite set of items, with the goal of assigning a representative vector to each one, possibly under some constraints (such as the collection of vectors being standardized, i.e., have zero mean and unit covariance). We are given data indicating that some pairs of items are similar, and optionally, some other pairs are dissimilar. For pairs of similar items, we want the corresponding vectors to be near each other, and for dissimilar pairs, we want the corresponding vectors to not be near each other, measured in Euclidean distance. We formalize this by introducing distortion functions, defined for some pairs of the items. Our goal is to choose an embedding that minimizes the total distortion, subject to the constraints. We call this the minimum-distortion embedding (MDE) problem. The MDE framework is simple but general. It includes a wide variety of embedding methods, such as spectral embedding, principal component analysis, multidimensional scaling, dimensionality reduction methods (like Isomap and UMAP), force-directed layout, and others. It also includes new embeddings, and provides principled ways of validating historical and new embeddings alike. We develop a projected quasi-Newton method that approximately solves MDE problems and scales to large data sets. We implement this method in PyMDE, an open-source Python package. In PyMDE, users can select from a library of distortion functions and constraints or specify custom ones, making it easy to rapidly experiment with different embeddings. Our software scales to data sets with millions of items and tens of millions of distortion functions. To demonstrate our method, we compute embeddings for several real-world data sets, including images, an academic co-author network, US county demographic data, and single-cell mRNA transcriptomes.

Before starting our quest for our best model, we want to find a dataset and a model first. We chose to use Amazon Us Reviews. The goal is to predict its target feature (the number of stars attributed) using customer reviews. Below, we're defining the model whose hyperparameters we will try to optimize: If you're not familiar with pipelines, don't hesitate to check out our previous article! Before we get to the optimization part, we first need to know what are our model's hyperparameters, right?